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Mathematics is a very important subject that students study in school. We need Mathematics in every aspect of our lives to solve reallife problems. Mathematics helps us solve reallife problems.
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ToggleClass 7 Mathematics Chapter 5, is about lines and angles. Students have learned about angles in previous chapters. They have learned about lines in past classes too. So, students won’t find this chapter tough because they have learned about the concepts before. But they should practice questions regularly to score better in exams.
Extramarks is a leading company that provides all the important study materials related to CBSE and NCERT. Our experts have made the Important Questions Class 7 Mathematics Chapter 5 to help students in practice. They collected the questions from different sources, such as the textbook exercises, CBSE sample papers, CBSE past years’ question papers, and important reference books. They have further checked the answers so students can easily understand the sums. Thus, it will help them score better in exams.
Extramarks is a leading company that provides all the important study materials. Every day, we assist thousands of students and teachers.Apart from important questions, we provide CBSE syllabus, CBSE extra questions, CBSE revision notes, CBSE sample papers, CBSE past years’ question papers, NCERT books, NCERT solutions, NCERT Exemplar, important formulas, and many more. You can download the study materials after registering on our official website.
Important Questions Class 7 Mathematics Chapter 5 – With Solutions
Extramarks is a leading company that provides all the necessary study materials related to CBSE and NCERT. Our experts have made this question series so that students can follow the questions and answers as well. The experts have collected the questions from sources such as textbook exercises, CBSE sample papers, CBSE past years’ question papers, NCERT exemplars, and important reference books. They have further solved the questions, and experienced professionals have further checked the answers to ensure the quality of the content. As a result, the Important Questions in Class 7 Mathematics Chapter 5 will assist students in performing better in exams.The important questions are
Question 1. Identify which of these following pairs of angles are complementary to each other and which of these angles are supplementary.
(i) 65, 115
Answer 1:
We have to find the sum of all the given angles to identify whether these angles are complementary or supplementary.
Now,
= 65 + 115
= 180
If the sum of the two angle measures is 180, then these two angles are said to be supplementary.
Hence, These angles are termed supplementary angles.
(ii) 63, 27
Answer:
We have to find the final sum of the given angles to identify whether these angles are complementary or supplementary.
So,
= 63 + 27
= 90
If the total sum of the two angle measures is 90, then these two angles are said to be complementary.
Hence, These angles are complementary angles.
(iii) 112, 68
Answer:
We have to find the sum of all the given angles to identify whether these angles are complementary or supplementary.
Then,
= 112 + 68
= 180
If the sum of the two angle measures is 180 degrees, then the two angles are said to be a supplementary.
Hence, These angles are supplementary angles.
(iv) 130, 50
Answer
We have to find the sum of all the given angles to identify whether these angles are complementary or supplementary.
Then,
= 130 + 50
= 180
If the sum of the two angle measures is 180 degrees, then these two angles are said to be supplementary to each other.
∴These angles are supplementary angles.
(v) 45, 45
Answer:
We have to find the sum of the given angles to identify whether these angles are complementary or supplementary.
Then,
= 45 + 45
= 90
If the sum of the two angle measures is 90, then the two angles are said to be complementary.
∴These angles are complementary angles.
(vi) 80, 10
Answer:
We have to find the sum of the given angles to identify whether these angles are complementary or supplementary.
Then,
= 80 + 10
= 90
If the sum of the two angle measures is 90 degrees, then the two angles are said to be a complementary angles.
Hence, These angles are complementary angles.
Question 2. Find the angles which are equal to the complement angle.
Answer 2:
Let the measure of a required angle be x degrees.
So, we know that the sum of measures of the complementary angle pair is 90.
Then,
= x + x = 90
= 2x = 90
= x = 90/2
= x = 45
Hence, the required angle measure is 45.
Question 3. Determine the angle which is equal to its own supplement angle.
Answer 3:
Let the measure of required angle be x degrees.
We know that the total sum of the measures of the supplementary angle pair is 180.
Then,
= x + x = 180
= 2x = 180
= x = 180/2
= x = 90
Hence, the required angle measure is 90.
Question 4. Can two angles be supplementary angles if both of them are:
(i). Acute?
Answer:
No. If two angles are acute angles, it means it is less than 90, which means that the two angles cannot be the supplementary angle because their sum will always be less than 90.
(ii). Obtuse?
Answer:
No. If the two angles are obtuse, then it means more than 90, so the two angles cannot be the supplementary angle. Because their sum will always be more than 180.
(iii). Right?
Answer:
Yes. If the two angles are right, which means both measure 90, then two angles can form a supplementary pair.
∴90 + 90 = 180
Question 5. An angle is greater than 45 degrees. Is its complementary angle greater than degree 45 or equal to 45 or less than degree 45?
Answer 5:
Let us assume that the complementary angles are p and q,
We know the sum of the measures of the complementary angle pair is 90.
Then,
= p + q = 90
It is given in the above question that p > 45
Adding q on both sides,
= p + q > 45 + q
= 90 > 45 + q
= 90 – 45 > q
= q < 45
Hence, its complementary angle is less than degree 45.
Question 6. Fill in the following blanks:
(i) If the two angles are known as complementary angles, the sum of their measures is _______.
Answer:
If the two angles are known as complementary angles, the sum of their measures is 90 degrees.
(ii) If the two angles are known as supplementary, so the sum of their measures is ______.
Answer:
If two of these angles are supplementary angles, then the sum of the measures is 180 degrees.
(iii) Two angles that form a linear pair are known as _______________.
Answer:
Two angles forming a linear pair are called the Supplementary angle.
(iv) If the two adjacent angles are supplementary, they form a ___________.
Answer:
If the two adjacent angles are supplementary angles, then they form a linear pair.
(v) If the two lines intersect at a given point, then the vertically opposite angles are always
_____________.
Answer:
If two lines intersect at a given point, then the vertically opposite angles present are always equal.
(vi) If two lines intersect at a given point, and if one pair of the vertically opposite angles are the acute angles, then the other pair of the vertically opposite angles are __________.
Answer:
If two lines intersect at a given point, and if one of the pair of the vertically opposite angles are the acute angles, then the other pair of the vertically opposite angles are Obtuse angles.
Question 7. If the complement of an angle is 79 degrees, then the angle will be
(i) 1 (ii) 11 (iii) 79 (iv) 101
Answer 7:
(ii) 11
Explanation
When the sum of the measures of any two angles is 90 degree, then the angles are called complementary angles. Each of them complements the other.
The given complement of an angle is 79
Let the measure of the angle be in degree x.
Then,
x + 79 = 90
x = 90 – 79
x = 11
Hence, the measure of the angle is 11.
Question 8. Angles which are both supplementary as well as vertically opposite are
(i) 95, 85 (ii) 90, 90 (iii) 100, 80 (iv) 45, 45
Answer 8:
(b) 90, 90
Explanation
When the sum of the measures of the two angles is 180 degree, then the angles are called as supplementary angles.
Question 9. The angle which makes a linear pair with an angle of 61 degree is of
(i) 29 (ii) 61 (iii) 122 (iv) 119
Answer 9:
(d) 119
Explanation
A linear pair is a pair of adjacent angles whose noncommon sides are the opposite rays.
We know that the measure of the sum of the adjacent angles is always equal to 180.
Let the measure of the other angle be x.
Then,
x + 61 = 180
x = 180 – 61
x = 119
Question 10. The angles x degree and 90 – x are
(i) supplementary (ii) complementary
(iii) vertically opposite (iv), making a linear pair
Answer 10:
(ii) complementary angle
Explanation
When the sum of the measures of the two angles is 90 degree, then the angles are called complementary angles.
x + 90 – x = 90
90 = 90
LHS = RHS
Question 11. The angles x – 10 degree and 190 – x are
(i) interior angles present on the same side of the transversal
(ii) making a linear pair
(iii) complementary
(iv) supplementary
Answer 11:
The correct option is (iv) supplementary
Explanation
When the sum of the measures of these two angles is 180 degree, then the angles are called as supplementary angles.
x – 10 + 190 – x = 180
190 – 10 = 180
180 = 180
LHS = RHS
Question 12. If the angle P and angle Q are supplementary angles and the measure of angle P is 60 degrees, then the measure of the angle Q is
(a) 120 (b) 60 (c) 30 (d) 20
Answer:
The correct option is (a) 120
Explanation
When the sum of the measures of these two angles is 180 degree, then the angles are called the supplementary angles.
P + Q = 180
60 + Q = 180
Q = 180 – 60
Q = 120
Question 13. The measure of the angle which is four times of its own supplement angle is
(a) 36 (b) 144 (c) 16 (d) 64
Answer:
The correct option is (b) 144
Explanation
We know that the final sum of measures of the two angles is 180 degrees, then the angles are called supplementary angles.
Let us assume that the angle is x.
Then, its supplement angle is = (180 – x)
As per the condition given in the above question, x = 4 (180 – x)
x = 720 – 4x
x + 4x = 720
5x = 720
x = 720/5
x =144
Question 14. The difference found between the two complementary angles is 30 degrees. Then, the angles present are
(a) 60, 30 (b) 70, 40 (c) 20, 50 (d) 105, 75
Answer:
(a) 60, 30
Explanation
When the sum of the measures of the two angles is 90 degrees, then the angles are called the complementary angles.
So, 60 + 30 = 90
As per the condition in the question, 60 – 30 = 30
Question 15. If the two supplementary angles are in the ratio of 1: 2, then the bigger angle is of
(a) 120 (b) 125 (c) 110 (d) 90
Answer:
(a) 120
Explanation
We know that the sum of the measures of the two angles is 180 degrees, then the angles are called the supplementary angles.
Let us assume that the two angles be 1x and 2x.
1x + 2x = 180
3x = 180
x = 180/3
x = 60
Then the bigger angle is 2x = 2 × 60 = 120
Question 16. Statements a and b are given below:
Statement a: If the two lines intersect at each other, then the vertically opposite angles present are equal in nature.
Statement b: If a transversal line intersects the two other lines, then the sum of the two interior angles present on the same side of the transversal is 180 degrees.
Then
(a) Both statements a and b are true
(b) Statement a is true while the statement b is false
(c) The statement a is false, and b is true
(d) Both statements a and b are false
Answer 16:
(b) Statement a is true while statement b is false
Question 17. In a pair of adjacent angles, the,
(i) vertex is always common,
(ii) one arm is always common, and
(iii) uncommon arms are always opposite rays
So,
(a) All the statements (i), (ii) and (iii) are true
(b) The statement (iii) is false
(c) The statement (i) is false, but the statements (ii) and (iii) are true
(d)The statement (ii) is false
Answer 17:
(b) The statement (iii) is false
Explanation Two angles are called adjacent angles only if they contain a common vertex and arm but no other common interior points.
Question 18. If an angle is 60 degrees less than the two times of its supplement, then the greater angle is of
(a) 100 (b) 80 (c) 60 (d) 120
Answer 18:
(a) 100
Explanation
Let us assume the angle is P.
Then, its supplement is 180 – P
As per the condition in the question,
P = 2(180 – P) – 60
P = 360 – 2P – 60
P + 2P = 300
3P = 300
P = 300/3
P = 100
So, its supplement is 180 – P = 180 – 100 = 80
Therefore, the greater angle is 100.
Question 19. In the below questions, fill in the blanks to make the below statements true.
 a) If the sum of the measures of the two angles present is 90 degrees, then the angles are _________.
Answer:
If the sum of measures of the two angles is 90 degrees, then these angles are complementary angles.
b). If the sum of measures of the two angles is degrees 180 , then they are _________.
Answer:
If the sum of measures of the two angles is 180 degrees, then they are supplementary angles.
c). A transversal that intersects two or more than the two lines at _________ points.
Answer:
A transversal always intersects two or more two lines at distinct points.
Question. If a transversal intersects the two parallel lines, then [from (a) to (d) ].
a). The sum of the interior angles present on the similar side of a transversal is.
Answer:
The Sum of interior angles on the similar side of a transversal is 180.
b). Alternate interior angles have one common.
Answer:
Alternate interior angles have one common arm.
c). Corresponding angles are on the side of the transversal.
Answer:
Corresponding angles are on the similar side of the transversal.
d). Alternate interior angles are on the side of the transversal.
Answer:
Alternate interior angles are present on the opposite side of the transversal.
e). Two lines that are present in a plane which does not meet at a given point anywhere are called lines.
Answer
Two lines present in a plane which do not meet together at a given point anywhere are called parallel lines.
f). Two angles forming a __________ pair are supplementary.
Answer:
Two angles forming a linear pair are supplementary
g). The supplement of an acute is always __________ angle.
Answer:
The supplement angle of an acute angle is always called an obtuse angle.
h). The supplement of a right angle is always _________ angle.
Answer:
The supplement angle of the right angle is always the right angle.
i). The supplement of an obtuse angle is always _________ angle.
Answer:
The supplement angle of an obtuse angle is always called an acute angle.
j). In a pair of complementary angles, each of these angles cannot be more than _________.
Answer:
In the pair of complementary angles, each angle present cannot be more than 90.
k). An angle is 45o. Its complementary angle will be __________.
Answer:
An angle is 45o. Its complementary angle will be 45.
l). An angle which is half of its supplement is of __________.
Answer:
An angle which is half of its supplement angle is the angle of 60.
Let us assume that the angle is p, and the supplement is 2p
Hence, p + 2p = 1800
3p = 1800
p = 600
Benefits of Solving Important Questions Class 7 Mathematics Chapter 5
Practice is very important for students. It helps them in several ways, and it also helps them score better in exams. The experts have collected the questions from different sources so that students can solve the questions regularly. The habit of regularly solving questions will help them score better on exams. There will be multiple benefits to solving the Important Questions Class 7 Mathematics Chapter 5. These are
 The experts have collected the questions from different sources, such as the textbook exercises, CBSE sample papers, CBSE past years’ question papers, and important reference books. Thus, students don’t have to search for answers from different sources; they will find them in a single article. Therefore, the Important Questions Class 7 Mathematics Chapter 5 will provide a large variety of question types, and if they solve the questions regularly, they can be better at the subject. Eventually, it will help them score better in exams.
 The experts have not only collected the questions, but they have solved the questions too. They followed a stepbystep process to explain each question so students could easily understand it. Thus, students can follow the answers if they cannot solve the questions. Furthermore, they can compare their answers with the answers provided by the experts. As a result, the Chapter 5 Class 7 Mathematics Important Questions will also assist them in better understanding the chapter material.It will help them generate interest in the subject matter. If they grow interested, they can answer the question regularly.
 Many students tend to be afraid of Mathematics. It is because they need to understand the subject matter properly. Practice will help students clear their doubts and easily understand the subject matter. Sometimes, the test book exercises have limited questions, and students must take help from other sources. The Important Questions Class 7 Mathematics Chapter 5 will help them because they will find different questions in this article. Apart from this, they will also find the answers. Thus, the question series will help them to generate interest in the subject matter, allow them to understand Mathematics better and increase their marks in exams.
Extramarks is a leading company that provides all the important study materials related to CBSE and NCERT. You may download the study materials after registering on our official website. We provide CBSE syllabus, CBSE extra questions, CBSE Revision notes, CBSE sample papers, CBSE past years’ question papers, NCERT books, NCERT solutions, NCERT Exemplars, NCERT important questions, vital formulas etc. Like the Mathematics Class 7 Chapter 5 Important Questions, you will also find important questions for other chapters. The links to the questions are given below
 NCERT books
 Important questions
 CBSE Revision Notes
 CBSE syllabus
 CBSE sample papers
 CBSE past years’ question papers
 Important formulas
 CBSE extra questions
Q.1 In the given figure, find the values of x, y, and z.
Marks:3
Ans
The given figure is:
From figure,
z = 90° (vertically opposite angles)
Now,
x, z, 30° lie on a straight line
By Linear Pair Axiom,
x + z + 30^{—¦ }= 180°
x + 90° + 30° = 180°
x + 120° = 180^{—¦}
x = 60°
And,
y = 30° (vertically opposite angles)
Hence, x = 60°, y = 30°, z=90°
Q.2 In the figure given below, PQ, RS, and UT are parallel lines.
$\mathrm{If}\text{measure of}\angle \mathrm{c}={57}^{}\mathrm{and}\text{}\angle \text{a =}\frac{\angle \mathrm{c}}{3}\text{, find the values of}\angle \text{a,}\angle \text{b and}\angle \text{d.}$
Marks:2
Ans
$\begin{array}{l}\mathrm{Given}\text{that :}\angle \mathrm{c}={57}^{}\text{and}\angle \text{a =}\frac{\angle \mathrm{c}}{3}\\ \therefore \angle \text{a =}\frac{{57}^{}}{3}{\text{= 19}}^{}\\ \mathrm{Since}\text{}\mathrm{PQ}\mathrm{UT},\\ \angle \mathrm{a}\text{}+\text{}\angle \mathrm{b}\text{}=\text{}\angle \mathrm{c}\left(\mathrm{alternate}\text{}\mathrm{interior}\text{}\mathrm{angles}\right)\\ \Rightarrow {19}^{}\text{+}\angle \text{b =}{57}^{}\\ \Rightarrow \angle \mathrm{b}\text{=}{57}^{}{19}^{}={38}^{}\\ \begin{array}{l}\mathrm{Also},\text{}\mathrm{PQ}\mathrm{RS}\left(\mathrm{Given}\right)\\ \angle \mathrm{a}\text{}+\text{}\angle \mathrm{d}\text{}=\text{}{180}^{}\left(\mathrm{co}\mathrm{interior}\text{}\mathrm{angles}\right)\\ {19}^{}+\text{}\angle \mathrm{d}\text{}=\text{}{180}^{}\end{array}\\ \angle \mathrm{d}\text{}=\text{}{180}^{}\u2013\text{}{19}^{}=\text{}{161}^{}\end{array}$
Q.3 (i) Find the angle, which is equal to its complement.
(ii) Find the angle, which is equal to its supplement.
Marks:2
Ans
(i) Let x be the required angle.
Then x+x = 90° ⇒ 2x= 90° ⇒ x= 45°
Therefore, the angle which is equal to its complement is 45°.
(ii) Let x be the required angle.
Then x+x = 180° ⇒ 2x= 90° ⇒ x= 90°
Therefore, the angle which is equal to its supplement is 90°.
Q.4 In the given figure, lines l and m are parallel. What is the value of x?
Marks:1
1. 30°
2. 60°
3. 90°
4. 120°
Ans
3. 90°
Explanation
In the given figure draw a line, which is parallel to l and m as shown below.
$\begin{array}{l}\angle 1=60\xb0\text{}\left(\mathrm{Alternate}\text{}\mathrm{angles}\right)\\ \angle 2=30\xb0\left(\mathrm{Alternate}\text{}\mathrm{angles}\right)\\ \therefore \mathrm{x}=\angle 1+\angle 2\\ =60\xb0+30\xb0\\ =90\xb0\end{array}$
Q.5 What is the value of x, if l  m?
Marks:1
1.36°
2. 30°
3. 45°
4. 90°
Ans
1. 36°
Explanation
$\begin{array}{l}\text{Since,}\mathrm{l}\u2013\mathrm{m}\\ \therefore 2\mathrm{x}+3\mathrm{x}=180\xb0\text{(cointerior angles)}\\ \Rightarrow 5\mathrm{x}=180\xb0\\ \Rightarrow \text{}\mathrm{x}=\frac{180\xb0}{5}=36\xb0\\ \text{Hence, the required value of}\mathrm{x}\text{is}36\xb0.\end{array}$
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FAQs (Frequently Asked Questions)
1. How can the Important Questions Class 7 Mathematics Chapter 5 help students?
Students often need more than textbook exercises. The textbook exercises consist of limited questions, and more than these are required. So, the experts at Extramarks have created the question series to help students. They collected the questions from different sources, such as the textbook exercises, CBSE sample papers, CBSE past years’ question papers, and important reference books. Apart from this, they have solved the questions, and experienced professionals have further checked the answers to ensure the best quality of the content. Thus, the Important Questions Class 7 Mathematics Chapter 5 will help students score better in exams. It will also help them generate interest in the subject matter and boost their confidence.